There's a gap of cultural understanding right there, I don't think they really know you want to "volunteer" unless you specifically say so. (then you might get your answer, yes or no) I'm not sure in what kind of context you mean. If you're talking about helping out the family if you're homestaying; it depends! Generally in the west you don't let your guests do any work, but if you're homestaying for a longer while you 'become part of the family'. To be part of the family you would have to function and help out with the work. I hope that makes sense. I'll try to sum it up in two sentences; You generally don't have to help out, offering your help is not wrong however! If you're 'part of the family' you can help out, but this may vary, depending on with whom you're staying.